info:eu-repo/semantics/article
The Lagrange-D'Alembert-Poincaré equations and integrability for the Euler's disk
Fecha
2007-01Registro en:
Cendra, Hernan; Diaz, Viviana Alejandra; The Lagrange-D'Alembert-Poincaré equations and integrability for the Euler's disk; Springer; Regular and Chaotic Dynamics; 12; 1; 1-2007; 56-67
1560-3547
1468-4845
CONICET Digital
CONICET
Autor
Cendra, Hernan
Diaz, Viviana Alejandra
Resumen
Nonholonomic systems are described by the Lagrange-D'Alembert's principle. The presence of symmetry leads, upon the choice of an arbitrary principal connection, to a reduced D'Alembert's principle and to the Lagrange-D'Alembert-Poincaré reduced equations. The case of rolling constraints has a long history and it has been the purpose of many works in recent times. In this paper we find reduced equations for the case of a thick disk rolling on a rough surface, sometimes called Euler's disk, using a 3-dimensional abelian group of symmetry. We also show how the reduced system can be transformed into a single second order equation, which is an hypergeometric equation.